Laser with reflective etalon tuning element

ABSTRACT

A tunable laser and laser tuning method based on the use of a tunable etalon in reflection as a mirror within a laser cavity and forming an end reflective surface thereof. The laser emission wavelength is not necessarily at a wavelength of peak etalon reflectivity. A preferred embodiment makes use of a microelectromechanical etalon to tune an external cavity semiconductor.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of application Ser. No.10/231,647, filed Aug. 29, 2002, now abandoned, the disclosure of whichis incorporated herein by this reference.

FIELD OF INVENTION

This invention relates to tunable lasers and to a method of tuninglasers using an etalon in reflection.

BACK GROUND OF THE INVENTION

A laser consists of a pumped gain medium placed within an opticalresonator.

The pumped gain medium provides optical amplification, and the opticalresonator provides optical feedback, such that light circulates withinthe optical resonator and is repeatedly amplified by the gain medium.Frequently the optical resonator is referred to as the laser cavity.Various pumps are known, the most common being optical pumps andelectrical pumps.

If the round trip loss within the optical resonator is less than theround trip gain provided by the gain element, the optical powerincreases on each round trip around the cavity. Since the amplificationprovided by the gain element decreases as the circulating optical powerincreases, the steady state circulating power is the power required tomake the round trip gain equal to the roundtrip loss. One of theelements within the optical resonator acts as the output coupler,whereby a certain fraction of the circulating power is emitted from theoptical resonator, and constitutes the laser output. A partiallytransmitting mirror is a typical output coupler. Of course, thewavelength of the light emitted by the laser need not be in the visiblepart of the electromagnetic spectrum.

An external cavity semiconductor laser is one type of laser. As lightmakes a round trip within an external cavity semiconductor laser, lightis emitted from an optically or electrically pumped semiconductor gainmedium, passes through various optical elements, and impinges on thegain medium as a reflected return beam. Typically, multiplesemiconductor layers are epitaxially grown on a semiconductor substrateto form the gain medium, and the gain medium waveguide is formed bylithographic processing of some or all of the epitaxially grown layers.The resulting waveguide is contiguous with the substrate. That is, thewaveguide is either in direct contact with the substrate or there areone or more intervening solid layers between the waveguide and thesubstrate. The epitaxially grown layers can have various compositions,which may or may not be the same as the composition of the substrate.

An optical beam emitted from a single-mode optical waveguide has anamplitude and phase profile (“mode profile”) which is determined by thewaveguide. The amplitude and phase profile of the return beam isgenerally not exactly the same as that of the mode profile, and in suchcases, not all of the return beam power is launched (i.e. coupled) intothe gain medium waveguide. For example, if a return beam having a powerPb impinges on the waveguide endface, only some lesser amount of powerPo is actually launched into the waveguide. The coupling efficiencyη=Po/Pb depends on how close the return beam amplitude and phase profileis to the mode profile. The waveguide gain medium therefore acts as anintracavity spatial filter.

The laser emission wavelength is the wavelength at which the net gain(i.e. gain loss) is maximal. If the gain medium provides amplificationover a wide wavelength range and the spectral dependence of the loss isdominant (i.e. the difference between minimum loss and maximum loss atdifferent wavelengths is large compared to the gain), then the laseremission wavelength will closely approximate the wavelength at which theround trip loss in the resonator is minimized. For example, if thewavelength of minimum loss is λo, and the laser emission wavelength isλ₁ the wavelengths λo and λ₁) will differ if the wavelength dependenceof the gain is strong enough that the round trip net gain is maximizedat a wavelength which differs only slightly from the wavelength ofminimum loss. Thus, the most common way to make a tunable laser is toinsert one or more optical elements within the laser cavity to create atunable intracavity bandpass filter. Since a tunable bandpass filterwill have a lower loss for a narrow range of optical wavelengthscentered about a center wavelength λ_(c), and higher loss forwavelengths outside this range, such a filter will tune the laseremission wavelength. In this case, the difference between λo and λ₁ willbe no larger than the filter bandwidth. The use of an etalon intransmission to provide an intracavity bandpass filter for laser tuningis known [e.g. Zorabedian et al. Optics Letters 13(10) p 826 (1988);U.S. Pat. No. 5,949,801 to Tayebati; U.S. Pat. No. 6,301,274 to Tayebatiet al].

An etalon comprises two substantially parallel, partially transmittingmirrors. It is known that etalon mirrors need not be exactly parallel toform an optical resonator. Transmission through an etalon is generallylow, except for a series of peaks, which are approximately equallyspaced at an interval known as the free spectral range of the etalon, asseen in FIG. 2 a. The center wavelength of an etalon transmission peakcan be varied by changing the optical distance between the etalonmirrors.

The optical distance d_(opt) between two points a and b is given by:d_(opt) = ∫_(a)^(b)n{x)𝕕xwhere n(x) is the position-dependent index of refraction.

It is necessary for the etalon free spectral range to be substantiallylarger than the desired tuning range, to ensure that only one of theetalon transmission peaks is within the desired tuning range. Thebandwidth of the transmission peaks is also an important parameter forlaser tuning, since bandwidth determines the loss seen by the modesadjacent to the lasing mode, which in turn determines the side modesuppression ratio (SMSR). Both the bandwidth and free spectral range ofan etalon can be varied according to known design principles.

Reflection from an etalon is generally high, except for a series ofvalleys of low reflectivity, which are approximately equally spaced atthe free spectral range, as seen in FIG. 2 b. As seen in FIGS. 2 a and 2b, the etalon reflectivity is high where the transmissivity is low, andvice versa. Because the reflection spectrum of an etalon does notprovide a narrow bandpass filter, an etalon would not be expected to actas a tuning element in reflection. See, for example, Siegman, Lasers.University Science Books, Mill Valley Calif. (1986), p 424, and U.S.Pat. No. 6,351,484 both of which describe the use of a reflective etalonas an output coupler for a high power laser. In this case, the etalon isnot acting as a tuning element but rather as a mirror.

In U.S. Pat. No. 5,901,163 a low finesse etalon is used as an endelement of the laser cavity, and its function is to work as an outputcoupler, but at the same time, to further narrow the laser line formedby the main tuning element (a diffraction grating). However, thisapplication is different from the present invention in several criticalaspects:

-   i) The etalon in the patent is used at the peak of its reflectivity.    The distortion of spatial distribution of the phase or the amplitude    of the reflected beam, has no impact on its operation. In the    present invention, the lasing occurs not at the peak of the etalon's    reflectivity, but rather close to the minimum of its reflectivity.    The reason for this is the distortion of spatial distribution of the    phase or the amplitude of the reflected beam.-   ii) The etalon of the patent may provide some additional narrowing    of the laser emission spectrum (in addition to that due to the    grating), but this is only possible for very low finesse of the    etalon, such that the reflection spectral dependence is a sinusoidal    function with a low peak value. For the operation of such an    additional narrowing element it is essential to have only two single    reflections from both surfaces. In the case of multiple beam    interference (high finesse), the reflection spectrum will look like    a plateau with narrow gaps. No additional narrowing will be provided    in such a high-finesse case. In the present invention, in contrast,    the finesse will be high, and again, the lasing occurs close to    narrow gaps in the reflectivity spectral dependence of the etalon.-   iii) The etalon design of the patent cannot, on its own, function as    a tuning element. In such case the laser output spectrum will    consist of several lines corresponding to the reflection peaks of    the etalon. It needs the diffraction grating as the main tuning    element, and one of its peaks has to be matched with the spectral    position of the grating peak. In the present invention, the etalon    can function as the only tuning element operating in reflection, as    the end reflector of the cavity.

SUMMARY OF THE INVENTION

The present invention is based on the surprising discovery that anetalon in reflection can act as an effective laser tuning element. Wehave found this to be true even in cases where the laser emissionwavelength is not a wavelength of peak etalon reflectivity. In apreferred embodiment of the present invention, an etalon with a mirrorseparation that is electrostatically adjustable by applying a voltage tothe etalon is used as the tuning element. The etalon mirror separationdetermines the laser emission wavelength.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows the round trip loss vs. wavelength for different laseralignments.

FIG. 2 a shows the transmissivity vs. wavelength for an etalon.

FIG. 2 b shows the reflectivity vs. wavelength for an etalon.

FIG. 3 is a schematic block diagram of an embodiment of the inventionwhere a grid fixing etalon is used to provide discrete tunability.

FIG. 4 shows the tuning behavior of a laser using an etalon inreflection according to the present invention.

FIG. 5 is a schematic block diagram of an embodiment of the presentinvention where the laser output is taken from the gain medium.

FIG. 6 is a schematic block diagram of an embodiment of the presentinvention where the laser output is taken from the etalon.

FIG. 7 is a schematic block diagram of an embodiment of the presentinvention where an optical modulator is butt coupled to the gain medium.

FIG. 8 is a schematic block diagram of an embodiment of the presentinvention where an optical modulator is monolithically integrated withthe gain medium.

DETAILED DESCRIPTION OF THE DRAWINGS

The physical basis of the tuning mechanism of the present invention canbe understood by reference to FIG. 1. Consider a laser with anintracavity spatial filter e.g., a waveguide and a reflective etalon,aligned for maximum output power when the beam distortion provided bythe etalon is zero. In this case the wavelength dependence of the roundtrip loss will be as indicated by curve 10 in FIG. 1. However, such aloss versus wavelength dependence will not tune the laser, since nointracavity bandpass filter is present. In addition, the laser will notlase close to the resonance peak of the etalon but rather emit a broadspectrum at the wings of the peak where the loss is lower.

Now consider the same laser, except that the cavity is “misaligned” fromthe condition of maximum output power, by slightly tilting the etalon.This will still not provide an intracavity band pass filter but the lossin such case will be higher as indicated by curve 11 in FIG. 1. However,there are various ways an etalon can provide beam distortion. Forexample, multiple reflections within an etalon generally impartdistortion to the reflected beam. Similarly, if the incident beamilluminates an edge of the etalon, or a localized defect within theetalon, the reflected beam will be distorted.

The introduction of beam distortion in a laser may further increase theround trip cavity loss. However, a reflective etalon only significantlydistorts the beam over a limited range of wavelengths centered at itsresonance wavelength λ_(c). Beam distortion provided by a reflectiveetalon compensates for the “misalignment” at a particular wavelength λ₀.In this situation, the wavelength dependence of the round trip loss willbe as indicated by curve 12 in FIG. 1. Due to the changed alignment ofthe laser, the background loss LI is necessarily larger than the lossLO. The round trip loss L at λo is less than LI due to the compensationof the cavity “misalignment” by beam distortion, and this creates theintracavity bandpass filter shown in FIG. 1. This intracavity bandpassfilter is tunable by changing the etalon center wavelength λ_(c). Notethat it is not necessary to vary the cavity alignment in order to tunethe laser.

The purpose of the intra-cavity spatial filter in the present inventionis to enhance (i.e. increase the difference between L and LI) thisbandpass filtering effect by making the cavity round trip loss a moresensitive function of both beam distortion and cavity alignment.Although it is theoretically possible to obtain adequate laser tuningvia this mechanism in the absence of a spatial filter, in practice anintra-cavity spatial filter is necessary in order to obtain a broadtuning range that is desirable for many laser applications. In anexternal cavity semiconductor laser, the single mode waveguide in thegain medium acts as an intracavity spatial filter.

Ordinarily, a laser cavity is aligned such that loss is minimized. Forexample, the standard procedure for alignment of an external cavitysemiconductor laser entails centering the beam on all optical elementsand aligning the return mirror for maximum retro reflection. We havefound that this conventional alignment method is not appropriate when areflective etalon is employed as a tuning element. Instead, a“misalignment” of the laser cavity, e.g. a small angular departure fromthe condition of maximum retro reflection at the etalon return mirror,and/or a decentering of the optical beam on the reflective etalon suchthat the beam is not entirely within the clear aperture of the etalon,is required to obtain good tuning performance. In practice, the requiredmis-alignment can be determined by starting with the conventionalalignment and then systematically changing the alignment whilemonitoring the single mode tuning range in order to maximize the tuningrange. Systematic optimization procedures of this type are known in theart.

FIG. 3 is a schematic view of a tunable laser constructed according toone embodiment of the invention. The electrically pumped semiconductorgain medium 14 includes a single mode optical waveguide 16 with anintracavity endface 15 and a second endface 17. The endface 15 isanti-reflection coated and/or tilted with respect to the axis ofwaveguide 16 to reduce its reflectivity. Light is emitted from endface15 and propagates into a collimation lens 18. In one experiment, thehorizontal and vertical beam divergences were approximately 12 and 32degrees respectively (full angle, half-maximum of intensity). However,these beam divergences are not believed to be critical parameters forpracticing the invention. The collimation lens 18 receives the diverginglight beam from endface 15 and transmits it to a grid fixing etalon 20.Preferably, lens 18 is selected and positioned such that the beamtransmitted to grid fixing etalon 20 is collimated. Methods forselecting and positioning lens 18 to perform this collimating functionare well known in the art. In one experiment, a Geltech 350390 lens(NA=0.65, f=2.75 mm) was found to be suitable.

The collimated beam is received by the grid fixing etalon 20. The gridfixing etalon 20 is useful in some embodiments of the invention torealize certain advantages, but it is not a required element forimplementing the reflective etalon tuning mechanism. For someapplications, a tunable laser is required to accurately tune to specificpredefined channels which are equally spaced in frequency. For suchapplications, it is desirable for the laser emission wavelength to bematched to a standardized frequency grid so that tuning the laser causesthe emission wavelength to move in discrete steps from one channel tothe next (referred to as “discrete tunability”), as opposed tocontinuous tuning or stepwise tuning that is not aligned to astandardized frequency grid. Since the transmission peaks of an etalon,as shown in FIG. 2 a, are equally spaced in frequency, the insertion ofan etalon with the appropriate free spectral range (e.g. 100 GHz or 50GHz) can provide discrete tunability.

In order to perform its intended function, the grid fixing etalon 20 inFIG. 3 is preferably inserted into the laser such that the etalonsurface normals make a small angle (preferably 1-10 degrees) withrespect to the cavity axis, to thereby ensure that the beams reflectedfrom the etalon surfaces do not efficiently couple into the lasercavity. The etalon finesse is preferably moderate (e.g. 2<finesse<10),and this value of finesse is chosen to provide low loss in transmissionthrough etalon 20, and the desired level of spectral selectivity. Sinceetalon 20 serves as an absolute wavelength reference for the laser, itis preferably fabricated using materials, such as fused silica, that aremechanically stable and temperature insensitive.

Discrete tunability can also be achieved by appropriately engineering asecond (parasitic) etalon that is already present within the cavity(e.g. an etalon formed by the two faces of a semiconductor gain chip) toperform the grid fixing function. It is also possible to pre-select theoverall optical path length of the laser cavity to provide discretetunability, since the longitudinal mode spacing of a laser is determinedby the round trip optical path length. If a grid fixing etalon is usedto provide discrete tunability, then it is advantageous to choose theoverall cavity length such that the grid formed by the cavity modes canbe at least approximately aligned to the grid determined by the gridfixing etalon. Similarly, it is also advantageous to ensure thatparasitic etalons, such as the etalon formed by the endfaces of the gainchip, create a grid that is alignable with the desired grid, to allow aless demanding specification to be placed on the endface reflectivities.

After passing through grid fixing etalon 20, the beam is received by alens 22, which transmits the beam to a tuning etalon formed by mirrors24 and 26. Preferably, lens 22 is selected and positioned so that thetransmitted beam is focused down to a beam waist located at or near thetuning etalon. Methods for selecting and positioning lens 22 to performthis function are well known in the art. In one experiment, a Geltech350280 lens (NA=0.15, f=18.4 mm) was found to be suitable.

Two mirrors 24 and 26 together form the reflective etalon tuningelement.

Mirror 24 is partially transmitting, such that light incident on mirror24 can couple into the cavity formed by mirrors 24 and 26. The mirror 24is positioned such that it is at or near the beam focus point created bythe lens 22. Since the etalon formed by mirrors 24 and 26 is used inreflection, mirror 26 can be partially transmitting. The opticaldistance between mirrors 24 and 26 is electrically controllable with avoltage source 28. Preferably, the free spectral range of the reflectiveetalon formed by mirrors 24 and 26 is larger than the desired tuningrange, which can, for example, vary from roughly 10 nm to 80 nmdepending on the application. The etalon bandwidth is preferably in therange 0.2 nm to 5 nm.

A preferred approach for providing the reflective etalon is the use ofmicroelectromechanical systems (MEMS) technology to fabricate mirrors 24and 26 on a common substrate where application of a voltage betweenmirrors 24 and 26 changes their separation electrostatically. Suchtunable MEMS etalons are known in the MEMS art, as are methods forobtaining the preferred free spectral ranges and bandwidths identifiedabove. In one experiment, the MEMS etalon had a 40 micron diameter, abandwidth of 1-2 nm, and was tunable from 1554 nm to 1571.5 nm.

An alternative approach for tuning the reflective etalon is the use ofan electro-optic material (e.g. lithium niobate, lithium tantalate or aliquid crystal) between the etalon mirrors, so that the optical pathlength between the mirrors can be electrically adjusted withoutphysically moving the mirrors. Another alternative approach for tuningthe reflective etalon is to alter the etalon temperature to therebychange the optical path length between the mirrors. The spacing betweenthe mirrors, and the refractive index of the material between themirrors are both temperature dependent, and temperature tunable etalonsare known in the art.

The beam which is reflected from the etalon formed by mirrors 24 and 26passes back through elements 22, 20 and 18 in succession, to impinge onwaveguide endface 15. A certain fraction of this light is coupled intowaveguide 16, propagates to endface 17 where it is reflected, andpropagates back to endface 15 to complete a cavity round trip.

FIG. 4 shows output optical spectra for a laser which is tuned by anetalon in reflection, and which has a 100 GHz grid fixing etalon in thecavity as shown in FIG. 3. Several curves are shown, one for eachwavelength to which the laser is tuned. A 10 nm tuning range and >50 dBside mode suppression ratio are obtained. The effect of the 100 GHz gridfixing etalon is seen in the regular spacing of the side mode peaks.

FIG. 5 shows an embodiment of the present invention wherein a singlelens 36 is used to collect light emitted from waveguide endface 15 andfocus it onto mirror 24 of the reflective etalon. Methods for selectingand positioning lens 36 to perform this function are known in the art.In addition, light that is emitted from endface 17 is coupled to asingle mode optical fiber 30 by coupling optics 32. Coupling optics 32typically includes one or more lenses to mode match the light emittedfrom endface 17 to the optical fiber 30, as well as an optical isolatorto protect the laser from back reflections. Various designs for couplingoptics 32 are known in the art. Note that as shown in FIG. 5, couplingoptics 32 and optical fiber 30 need not be inside the laser cavity 34.

FIG. 6 shows another embodiment of the present invention where the laseroutput is obtained by transmission through the reflective etalon formedby mirrors 24 and 26. In this case, it is necessary for mirror 26 to bepartially transmitting.

FIG. 7 shows another embodiment of the present invention where anoptical modulator 38 is placed between output endface 17 and couplingoptics 32. Optical modulator 38 is a waveguide device including awaveguide 40. Optical modulator 38 is preferably placed sufficientlyclose to gain element 14 that light emitted from waveguide endface 17 isefficiently coupled into waveguide 40 without requiring coupling opticsto be placed between gain element 14 and optical modulator 38. Suchcontiguous positioning is referred in the art to as butt coupling.Modulated light emitted from modulator 38 is coupled to output fiber 30by coupling optics 32.

FIG. 8 shows another embodiment of the present invention where a gainelement and a modulator are monolithically integrated onto onesemiconductor chip 42. Waveguide reflector 46 defines the output couplerof laser cavity 34. Light emitted from waveguide reflector 46 enterswaveguide 44. Modulated light emitted from chip 42 is coupled to outputfiber 30 by coupling optics 32. There are several ways to providewaveguide reflector 46. One approach is to physically etch away materialbetween waveguides 16 and 44, in which case waveguide reflector 46functions as an endface. A second approach is to insert a Braggreflector between waveguides 16 and 44, so that the Bragg reflectorfunctions as waveguide reflector 46.

For many tunable laser applications, it is desirable to use controlsignals to set output power and output wavelength to specific desiredvalues. In the embodiments given above, an output power reference signalcan be obtained by monitoring a parasitic beam, such as a beam reflectedfrom grid fixing etalon 20 or a beam transmitted through mirror 26.These parasitic beams can also be used to provide a wavelength referencesignal, one known approach being to split a parasitic beam with a beamsplitter, pass one portion of the split beam through an optical filter,then compare filtered and unfiltered intensity to derive a wavelengthreference signal.

As is evident from the preceding description, the present inventionprovides a novel laser and laser tuning mechanism, of which a preferredembodiment is a laser tuned by a MEMS reflective etalon. As such, itwill be apparent to one skilled in the art that various modifications tothe details of construction and method shown here may be made withoutdeparting from the scope of the invention, e.g. folding the optical pathwithin the laser cavity and/or tuning element in order to make the lasermore compact. It will also be apparent to those skilled in the art thatthe operating principles that govern the selection of a singleoscillation frequency for a tunable laser can also be employed to obtainnon-tunable single frequency operation of a laser. Furthermore, etalonsneed not consist of two separate mirrors. It is known that etalons canbe formed by monolithic dielectric and/or semiconductor multilayerstructures, and such etalons can be tuned, e.g. by varying thetemperature of the etalon.

The previously disclosed embodiments have made use of a semiconductorgain medium in the form of a single mode optical waveguide, since thehigh gain and spatial filtering provided by such a configuration arepreferred. However, the present invention is also applicable to verticalexternal cavity surface emitting lasers, where the gain medium takes theform of an optically or electrically pumped semiconductor structureadapted for vertical emission of radiation from its top surface (asopposed to a waveguide endface).

Various embodiments have been given which show how the present inventionmay be combined with an external optical modulator to provide an opticaltransmitter. It is also possible for the laser of the present inventionto be directly modulated by varying the pumping supplied to the gainmedium in accordance with a data signal, using well known methods. Theembodiment of FIG. 5 is preferred for direct modulation, since high datarate direct modulation requires a short laser cavity, and the lasercavity length can be minimized most effectively in the simpleconfiguration of FIG. 5.

The foregoing detailed description of the invention includes passagesthat are chiefly or exclusively concerned with particular parts oraspects of the invention. It is to be understood that this is forclarity and convenience, that a particular feature may be relevant inmore than just the passage in which it is disclosed, and that thedisclosure herein includes all the appropriate combinations ofinformation found in the different passages. Similarly, although thevarious figures and descriptions herein relate to specific embodimentsof the invention, it is to be understood that where a specific featureis disclosed in the context of a particular figure or embodiment, suchfeature can also be used, to the extent appropriate, in the context ofanother figure or embodiment, in combination with another feature, or inthe invention in general. Further, while the present invention has beenparticularly described in terms of certain preferred embodiments, theinvention is not limited to such preferred embodiments. Rather, thescope of the invention is defined by the appended claims.

1. A tunable laser comprising: (a) a laser pump; (b) a resonant opticalcavity having a round trip light path, said optical cavity having an oddnumber of reflective surfaces and comprising: i) a gain mediumresponsive to pumping by said laser pump, one face of said gain mediumforming a first reflective endface of the resonant optical cavity; andii) a tuning etalon, positioned within the resonant optical cavity, saidetalon comprising two spaced apart mirrors having a controllablemirror-to-mirror separation distance, and forming the other reflectiveendface of said optical cavity, so that light traveling on said roundtrip light path is reflected from the etalon, and whereby the emissionwavelength of the gain medium is determined by a selected separationdistance of the etalon mirrors and is selected to have a value thatdiffers from a wavelength of peak reflectivity of the etalon, andwherein said gain medium comprises an electrically pumped, single-mode,semiconductor optical waveguide.
 2. The laser of claim 1, wherein saidetalon further comprises a microelectromechanical device with anelectrically adjustable free spectral range.
 3. The laser of claim 2,further comprising a lens positioned between said gain medium and saidetalon.
 4. The laser of claim 2, further comprising an optical fiber andcoupling optics positioned between said gain medium and the opticalfiber.
 5. The laser of claim 2, further comprising an optical fiber andcoupling optics positioned between said etalon and the optical fiber. 6.The laser of claim 2, further comprising means for generating awavelength reference signal.
 7. The laser of claim 2, further comprisingmeans for generating an output power reference signal.
 8. The laser ofclaim 2, wherein said pump has an output power that is variable inresponse to receipt of a data signal to provide a modulated pump outputsignal.
 9. The laser of claim 2, further comprising an optical fiber andan optical modulator positioned between said resonator and the opticalfiber.
 10. The laser of claim 9, wherein said optical modulator iscontiguous with said semiconductor substrate.
 11. The laser of claim 9,wherein said optical modulator is butt-coupled to said gain medium.